contestada

Describe in words the region of 3 represented by the equations or inequalities. x2 + z2 ≤ 49 Here x2 + z2 ≤ 49 or equivalently x2 + z2 ≤ 7 which describes the set of all points in 3 whose distance from the -axis is at most . Thus, the inequality represents the region consisting of all points on or inside a of radius with axis the -axis

Respuesta :

fabivelandia

Answer:

Here x² + z² ≤ 49 which describes the set of all points whose distance from the y-axis is at most 7 .Thus, the inequality represents the region consisting of all points on or inside a circular cylinder of radius 7 with axis the Y-axis

Step-by-step explanation:

The equation given is equivalent to [tex]\sqrt{x^2+z^2}\leq 7[/tex]. This square root, by the pythagorean theorem, represents the distance of a point (x,y,z) to the y axis( that is, to the point (0,y,0) ). There are no constraints in y, so for a fixed value of y, these points lie inside the plane of height y and inside the circle of radius 7 centered at (0,y,0). Taking y as a variable, we join all of these circles alongside the y- axis and obtain a cylinder of radius 7.

Otras preguntas